Parameterization of All Output-Rectifying Retrofit Controllers

TL;DR

This paper provides a comprehensive parameterization of all output-rectifying retrofit controllers, enabling easier design and understanding of structured controllers in distributed systems, by generalizing existing methods through state projection and inverse systems.

Contribution

It introduces a tractable, generalized parameterization of output-rectifying retrofit controllers applicable to the general output-feedback case, expanding previous constrained approaches.

Findings

All retrofit controllers can be characterized as a constrained Youla parameterization.

An unconstrained parameterization is derived under a technical measurability assumption.

Output-rectifying retrofit controllers can be designed even in the general output-feedback case.

Abstract

This study investigates a parameterization of all output-rectifying retrofit controllers for distributed design of a structured controller. It has been discovered that all retrofit controllers can be characterized as a constrained Youla parameterization, which is difficult to solve analytically. For synthesis, a tractable and insightful class of retrofit controllers, referred to as output-rectifying retrofit controllers, has been introduced. An unconstrained parameterization of all output-rectifying retrofit controllers can be derived under a technical assumption on measurability of particular signals. The aim of this note is to reveal the structure of all output-rectifying retrofit controllers in the general output-feedback case. It is found out that the existing developments can be generalized based on the notions of state projection and an inverse system. The result leads to the conclusion that output-rectifying retrofit controllers can readily be designed even in the general case.